ar X iv : p hy si cs / 0 61 22 50 v 1 29 D ec 2 00 6 The falling chain of Hopkins , Tait , Steele and Cayley

A uniform, flexible and frictionless chain falling link by link from a heap by the edge of a table falls with an acceleration g/3 if the motion is nonconservative, but g/2 if the motion is conservative, g being the acceleration due to gravity. Unable to construct such a falling chain, we use instead higherdimensional versions of it. A home camcorder is used to measure the fall of a threedimensional version called an xyz-slider. After frictional effects are corrected for, its vertical falling acceleration is found to be ax/g = 0.328 ± 0.004. This result agrees with the theoretical value of ax/g = 1/3 for an ideal energy-conserving xyz-slider. PACS numbers: 01.55.+b,01.65.+g,01.50.Zv The falling chain of Hopkins, Tait, Steele and Cayley 2 Figure 1. (a) The falling chain called the xy-slider that has one end fixed at the origin O of the coordinate system. The chain slides along the table edge after release. The falling chain is called an xyz-slider when the stationary segment on the table parallel to the edge is set back from the edge by a distance z = d. (b) The forces acting on the chain bend of the xy-slider at a sharp table edge.